8 citations · 21 across the 4 of their papers we have counts for
5 papers
Upper bounds for integer solutions to a system of two bilinear forms
Eugen Keil
We show that the number of integer solutions for a pair of bilinear equations in at least 2*6 variables has (up to logarithms) the expected upper bound unless there is a structural…
Some refinements for translation invariant quadratic forms in dense sets
Eugen Keil
We improve the result of our previous paper on translation invariant quadratic forms in two special cases. We reduce the density bound to $…
Moment estimates for exponential sums over k-free numbers
Eugen Keil
We investigate the size of L^p-integrals for exponential sums over k-free numbers and prove essentially tight bounds.
Translation invariant quadratic forms in dense sets
Eugen Keil
We generalize Roth's theorem on three term arithmetic progressions to translation invariant quadratic forms in at least 17 variables. We use Fourier-analysis, restriction theory, u…
On a diagonal quadric in dense variables
Eugen Keil
We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets A \subset Z and show quantitative bounds on the size of A if…